1. Field of the Invention
The present invention relates to a method of converting an electric analog signal into digital signals by using a non-linear A/D converter.
2. Background of the Invention
Various methods of converting an analog signal into digital signals have been put into practical use. In an image signal processing system, the original image on paper, a microfilm or the like is scanned by laser light, and the reflected or transmitted laser light is photoelectrically converted into an image signal. The analog image signal is subjected to A/D conversion to generate digital image signals which are subjected to gradation compensation, edge emphasis or other digital processing. In such image signal processing, it is always necessary to convert the analog image signal into digital image signals having digital values reflecting the density of the original image in order to make a sharp and clear reproduced image with fidelity to the original image. However, if the digital signals converted from the analog image signal have been digitized with too few bits, then in the digital electric processing, the continuously changing density of the original image is represented by a discontinuously changing density of the reproduced image due to the quantization error so that the quality of the reproduced image conspicuously deteriorates. For that reason, the A/D conversion needs to be performed with sufficiently fine digitization intervals. Since the density interval which can be perceived by human eyes differs between the light and the dark side, the deterioration of the quality of the reproduced image due to the discontinuity of the density can be minimized if the A/D conversion is performed with a minimum necessary number of bits depending on this difference. Examples of functions for representing the human visual characteristic are mentioned below:
CIE 1976: L*=116 (Y/Y.sub.o).sup.1/3 -16 PA1 Bartleson: L**=11.15 (100Y/Y.sub.o).sup.1/2 -16
The A/D conversion can be performed with N bit digitization over a density range from the maximum density D.sub.max to the minimum density D.sub.min on the basis of the relation between the above-mentioned function and the density so that the change .DELTA.L* in the human visual characteristic with regard to the digitization interval is constant [(L*.sub.max -L*.sub.min)/(2.sup.N -1)]. This variable quantization is ideal and the deterioration of the quality of the reproduced image can be avoided.
FIG. 1 shows curves each indicating the relation between the density D of a reproduced image and the density interval .DELTA.D with eight bit digitization. The density D is shown along the abscissa and the density interval .DELTA.D is shown along the ordinate in FIG. 1. Curves I and II indicate ideal cases of .DELTA.L* and .DELTA.L** respectively being held constant. For the ideal cases, the density range of between 0 and 2.4 is illustrated.
Usually, the density is subjected to near A/D conversion (with digitization of eight bits, for example). Curve III indicates the relation between the density and the density interval in the linear A/D conversion. It is understood from the ideal curves I and II and the linear curve III that the density can be finely divided at its lower portion (light side) but is roughly divided at its higher portion (dark side). Therefore, the density interval becomes larger at the higher end of the density due to the human visual characteristic.
Since the human visual characteristic is often considered to be logarithmic, the A/D conversion is thus performed in some cases after logarithmic conversion. Curve IV indicates the relation between the density and the density interval in the logarithmic conversion over the same density range. It is understood from the logarithmic curve IV that it is nearer to the ideal curves I and II. However, this density is divided at its higher end more finely than the actual resolving power of the human eye so as to make the density appear to be smoothly changing, but the discontinuity of the density looks conspicuous at its lower end.
Although it is impossible that the human visual characteristics L* and L** indicated by the ideal curves I and II are attained through the use of an electric circuit, an approximation to the characteristics can be expected to be performed to provide an improved characteristic to enhance the quality of a reproduced image. For the approximation, the use of an A/D converter having a non-linear conversion characteristic has been conventionally tried. The nonlinear A/D converter is now briefly described with reference to FIGS. 2A and 2B. FIG. 2A shows the basic circuit constitution of the conventional nonlinear A/D converter 10. A converting section (ADC) 12 converts an input analog signal into output digital signals. The output terminal of a first amplifier 14 is connected to the signal input terminal V.sub.IN of the converting section 12. The negative terminal of the first amplifier 14 is connected to an image signal input terminal 16 through a resistor R.sub.1, and the positive terminal of the first amplifier is grounded. A feedback resistor R.sub.2 is connected between the negative terminal and output terminal of the first amplifier 14. The negative terminal of the first amplifier 14 is connected to a power supply through an offset adjustment resistor R.sub.O. The output terminal of a second amplifier 18 is connected to the reference input terminal V.sub.REF of the converting section 12. The negative terminal of the second amplifier 18 is connected to the image signal input terminal 16 through a gain adjustment resistor R.sub.G and is also connected to the power supply through a bias adjustment resistor R.sub.B. A feedback resistor R.sub.3 connects the output terminal and the negative input terminal of the second amplifier 18. The positive terminal of the second amplifier 18 is grounded. The conversion output signal z of the nonlinear A/D converter 10 an be expressed as EQU z=(2.sup.N -1).times./(ax+b)
where x denotes an input image signal, ax+b denotes a reference signal, N denotes the number of bits in digitization, a coefficient a is determined by the gain, and another coefficient b is determined by the bias.
If N is given as a value of 8, the above equation becomes EQU z=255.times./(ax+b)
Therefore, z=0 results from x=0. If x=ax+b is given i.e. x=b/(1-a), z=255 results. If a and b are approximately determined, digital outputs .DELTA.d.sub.1 and .DELTA.d.sub.2 (.DELTA.d.sub.1 =.DELTA.d.sub.2) can be obtained for analog inputs .DELTA.a.sub.1 and .DELTA.a.sub.2 (.DELTA.a.sub.1 .noteq..DELTA.a.sub.2), thus enabling equal division, as shown in FIG. 2B which indicates the conversion characteristic of the nonlinear A/D converter. The analog inputs to the converter 12 and the digital outputs therefrom are shown along the abscissa and the ordinate, respectively, in FIG. 2B. It is understood from FIG. 2B that the resolving power for the digital output from the nonlinear A/D converter can be altered depending on the level of the analog input.
When the nonlinear A/D converter 10 having the above-described conversion characteristic is provided in an image signal processor, the visual discontinuity of a reproduced image, which has been a problem in the conventional art, can be reduced to make the density or gradation of the image look to be naturally changing to human eyes.
However, when the nonlinear A/D converter is used, the nonlinear conversion characteristic is affected by the irregularities of the components of the image signal processor so that the conversion characteristic varies from processor to processor. For that reason, there is a problem that reproduced images of the same density cannot be obtained when the identical original image is read by different processors.